(a)
The subspace of
The invertible matrices span the space of all
Given:
Calculation:
It is noted that a set of vectors spans a whole space if their linear combinations fill the space.
Therefore, the invertible matrices span the space of all
(b)
The subspace of
The rank one matrix span the space of all
Given:
Calculation:
It is noted that rank of a matrix is its number of pivots. If the rank one matrix has only one pivot, it means that its
Therefore, the rank one matrix spans the space of all
(c)
The subspace of
I itself spans the space of all multiples
Given:
Calculation:
It is noted that the identity matrix itself spans the space of all matrices.
Therefore, I by itself spans the space of all multiples
(b)
The subspace of
The rank one matrix span the space of all
Given:
Calculation:
It is noted that rank of a matrix is its number of pivots. If the rank one matrix has only one pivot, it means that its
Therefore, the rank one matrix spans the space of all
(c)
The subspace of
I itself spans the space of all multiples
Given:
Calculation:
It is noted that the identity matrix itself spans the space of all matrices.
Therefore, I by itself spans the space of all multiples
(c)
The subspace of
I itself spans the space of all multiples
Given:
Calculation:
It is noted that the identity matrix itself spans the space of all matrices.
Therefore, I by itself spans the space of all multiples
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Introduction to Linear Algebra, Fifth Edition
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